With the development of 6G wireless communication technologies, various resource-intensive and delay-sensitive vehicle application tasks are generated. These application tasks can be offloaded to Mobile Edge Computing (MEC) which deploys computing resources at the edge of networks. Besides, the recent proposed Cybertwin, as the digital representation of the complicated physical end-systems, can help the terminals obtain the required services from networks. Vehicles enabled by Cybertwin can offload their tasks to MEC and achieve better performance. In this paper, we focus on the study of a hybrid energy-powered multi-server MEC system with Cybertwin. Vehicles enabled by Cybertwin and edge servers send the current network status and unprocessed vehicle application tasks to the macro base station (MBS) to achieve the better allocation of resources. Energy harvesting (EH) devices are deployed on edge servers to form a “green energy-grid” hybrid energy supply model. We formulate a stochastic offloading optimization problem, and the goal is to minimize the system cost. The stochastic optimization problem is decomposed into three subproblems. Then, we design an efficient multi-vehicle task offloading (EMT) algorithm to achieve the trade-off between system cost and task queue length. Theoretical analysis shows that EMT algorithm can optimize the total cost of the MEC system and guarantee the system performance. According to experimental evaluation, we verify the performance of the EMT algorithm.